An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Programming Problems

Sakawa, M., Yumine, T., & Yano, H. (1984). An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Programming Problems. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-018

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Abstract

In this paper, we present a new interactive fuzzy satisficing method for solving multiobjective nonlinear programming problems by considering that the decision maker (DM) has fuzzy goals for each of the objective functions. The fuzzy goals of the DM are quantified by eliciting corresponding membership functions through the interaction with the DM. After determining the membership functions, if the DM specifies his reference membership values, the Tchebycheff norm problem is solved and the DM is supplied with the corresponding Pareto optimal solution and the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his reference membership values. In this way the satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his reference membership values. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated together with the computer outputs.

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